They don't want anyone else to be able to use the phrase "App Store" to refer to a place where you can buy apps.

Although, Jobs himself used the term generically. From the legal filing (excerpted from The Register [theregister.co.uk]):

"Apple further admits that its CEO, Steve Jobs, in October 2010 called the APP STORE service 'the easiest-to-use largest app store in the world, preloaded on every iPhone'."

While IANAL, I take the phrase "easiest-to-use, largest app store" to imply that there are others - presumably, smaller, harder to use - but, hey, that's just me, parsing English... Further quoting The Register article and filing - and this seems funny to me (emboldening mine):

Case in point: the filing also concedes that the Oxford English Dictionary defines an app as "[a]n application, esp. an application program," and that a store is, indeed, "a retail establishment selling items to the public: a health-food store."

These statements would seem to admit the obvious: that an app store is a store that sells apps. Apple, however, argues the opposite."Apple denies that, based on their common meaning, the words 'app store' together denote a store for apps," the filing reads.

About what other possible meaning the words "app store" might have, the Cupertinian oracle is silent.

Ahahahaha, oh my. Seriously? You fail reading comprehension, my lefty comrade. You fail hard. And you must not be much of a leftist AT ALL, or you would know what the term means. "Hippie punching" refers not to any sort of physical violence, it refers to the fact that even on the left, politicians try to find someone to the left of them to attack.

When Rahm Emmanuel called leftists "Fucking retards," THAT was hippie punching. In fact, there was a huge shitstorm over it where just about everyone on the left was using the term "hippie punching" and accusing the White House of it. Sorry we forgot to call and tell you about all the fun.

When I was volunteering with Food Not Bombs in San Francisco and the cops threw me to the ground, stood on my shoulder blades, zip-tied my hands and pulled up HARD on my arms, that was not hippie punching. That was just plain old police violence.

See the difference? Generally, only those on the left get accused of hippie punching, because on the right, it is just par for the course. Man bites dog and all that.